When the field goes barren and the villagers are planting and watering, does it matter how busy you keep them with those tasks or will the field start producing again if I let them do research or building during that "season."

whoohooo i was the 2 person to post in this forum and about your question my palm doesnt work with ldw's games )=

Elaine, your villagers will continue to gain farming skill as they perform farming activities, even when the farm is between crops. That extra skill will be very valuable later on in the game when you'll need a larger food supply. You could always divert your farmers to other tasks during that time and see what happens!